Methods and Apparatus for Obtaining Diagnostic Information Relating to an Industrial Process

1. A diagnostic apparatus for use in relation to an industrial process, the apparatus comprising a data processing apparatus programmed to: receive object data for a set of physical product units that have been subjected nominally to the same industrial process, the object data for each product unit representing one or more parameters measured on the product unit at points spatially distributed across the product unit; define a multidimensional space in which the object data for each of the product units can be represented as a vector; perform a multivariate analysis on the object data to obtain one or more component vectors in the multidimensional space; extract diagnostic information about the industrial process at least partly using certain one or more product units identified out of the set of product units based on the position of the respective vector of the identified one or more product units when projected onto one or more of the component vectors; and based on the diagnostic information, output electronic data for configuration or modification of the industrial process or of a measurement process of product units subjected to the industrial process.

2. An apparatus as claimed in claim 1 , arranged to receive for use as the object data spatially distributed measurements of one or more selected from: overlay, critical dimension, side wall angle, substrate quality, and/or focus.

3. An apparatus as claimed in claim 1 , arranged to extract diagnostic information based on the one or more identified product units whose respective vector occupies an outlying position when projected onto a selected one of the component vectors.

4. An apparatus as claimed in claim 1 , further arranged to receive context data representing one or more parameters of the industrial process as applied to each individual product unit, and further programmed to extract diagnostic information using the context data.

5. An apparatus as claimed in claim 4 , programmed to extract the diagnostic information at least partly by identifying a correlation between an identification of product units as being of interest based on the component vectors and one or more parameters in the context data.

6. An apparatus as claimed in claim 4 , programmed to extract diagnostic information by displaying one- or more-dimensional plots of product unit distribution with selected parameters from the context data, the product units being represented in the plots in such a way that product units designated as being of interest can be distinguished visually from other product units.

7. An apparatus as claimed in claim 1 , adapted for use where the industrial process includes performing one or more lithographic, physical and/or chemical operations by different individual processing apparatuses on different individual product units, and wherein the context data includes at least one parameter identifying the individual processing apparatus used for a given operation.

8. An apparatus as claimed in claim 1 , wherein the data processing apparatus is further configured to, for the extraction of diagnostic information: receive object data for one or more further product units that have been subjected nominally to the same industrial process as the set of product units, the object data for the further product unit(s) representing the one or more parameters measured on the further product unit(s) at points spatially distributed across the further product unit(s) with a lower density than the measurements received for the set of product units and such object data referred to as sparse object data, analyze the sparse object data by reference to at least a subset of the component vectors identified by the multivariate analysis, and combine the sparse object data with the component vectors in accordance with the result of the analysis of the sparse object data, in order to reconstruct object data representing the one or more parameters measured on the further product unit(s) at points spatially distributed across the further product unit(s) with a higher density than the sparse object data.

9. An apparatus as claimed in claim 8 , wherein the analysis of the sparse object data is performed by reference to sparse versions of the component vectors, each sparse version of a component vector being generated by sub-sampling the component vector in accordance with the spatial distribution of the sparse object data.

10. An apparatus as claimed in claim 1 , further programmed to generate correction data for use in controlling the industrial process.

11. An apparatus as claimed in claim 10 , further programmed to generate context criteria for use in determining to which product units the correction data should be applied by comparing the context criteria to further context data describing parameters of the industrial process as applied to the further product units.

12. An apparatus as claimed in claim 10 , adapted for use where the industrial process comprises a mixture of lithographic patterning operations and physical and/or chemical operations, and programmed to generate the correction data for applying corrections in a lithographic patterning operation.

13. An apparatus as claimed in claim 1 , further comprising a controller arranged to control an apparatus of the industrial process by applying corrections based on the extracted diagnostic information.

14. A method of obtaining diagnostic information relating to an industrial process, the method comprising: obtaining object data for a set of physical product units that have been subjected nominally to the same industrial process, the object data for each product unit representing a residual resulting from one or more parameters measured on the product unit at points spatially distributed across the product unit being subjected to a correction obtainable in the industrial process; defining a multidimensional space in which the object data for each of the product units can be represented as a vector; performing, by a hardware computer, a multivariate analysis on the object data to obtain one or more component vectors in the multidimensional space; extracting diagnostic information about the industrial process using the component vectors; and based on the diagnostic information, outputting electronic data for configuration or modification of the industrial process or of a measurement process of product units subjected to the industrial process.

15. A method as claimed in claim 14 , wherein the industrial process comprises a sequence of one or more lithographic processing steps performed on product units in the form of substrates, each lithographic processing step comprising one or more lithographic patterning operations followed by one or more physical and/or chemical processing operations.

16. A method as claimed in claim 14 , further comprising generating one or more sets of correction data for use in controlling the industrial process when performed on further product units.

17. A method as claimed in claim 14 , wherein the extracting diagnostic information comprises: receiving object data for one or more further product units that have been subjected nominally to the same industrial process as the set of product units, the object data for the further product unit(s) representing the one or more parameters measured on the further product unit(s) at points spatially distributed across the further product unit(s) with a lower density than the measurements received for the set of product units and such object data referred to as sparse object data, analyzing the sparse object data by reference to at least a subset of the component vectors identified by the multivariate analysis, and combining the sparse object data with the component vectors in accordance with the result of the analyzing, in order to reconstruct object data representing the one or more parameters measured on the further product unit(s) at points spatially distributed across the further product unit(s) with a higher density than the sparse object data.

18. A method of controlling a lithographic apparatus wherein corrections are applied based on diagnostic information extracted from object data by the method as claimed in claim 14 .

19. A non-transitory computer program product comprising machine readable instructions for causing a general purpose data processing apparatus to: receive object data for a set of physical product units that have been subjected nominally to a same industrial process, the object data for each product unit representing one or more parameters measured on the product unit at points spatially distributed across the product unit; define a multidimensional space in which the object data for each of the product units can be represented as a vector; perform a multivariate analysis on the object data to obtain one or more component vectors in the multidimensional space; extract diagnostic information about the industrial process at least partly using certain one or more product units identified out of the set of product units based on the position of the respective vector of the identified one or more product units when projected onto one or more of the component vectors; and based on the diagnostic information, output electronic data for configuration or modification of the industrial process or of a measurement process of product units subjected to the industrial process.

20. The computer program product of claim 19 , wherein extraction of diagnostic information comprises: receipt of object data for one or more further product units that have been subjected nominally to the same industrial process as the set of product units, the object data for the further product unit(s) representing the one or more parameters measured on the further product unit(s) at points spatially distributed across the further product unit(s) with a lower density than the measurements received for the set of product units and such object data referred to as sparse object data, analysis of the sparse object data by reference to at least a subset of the component vectors identified by the multivariate analysis, and combination of the sparse object data with the component vectors in accordance with the result of the analysis, in order to reconstruct object data representing the one or more parameters measured on the further product unit(s) at points spatially distributed across the further product unit(s) with a higher density than the sparse object data.